I really liked the idea, congratulations. I found a white egg at the beginning :) And I think there is a bug, sometimes when the phase restarts the agents do not return to their starting positions, obliging the player to reset the room.
that is not a bug, they are supposed to restart at the points where they were last flipped. I was originally going to use this mechanic in one of the levels, but I forgot to. Good job on finding the egg!